Method for Improving Synchronization and Information Transmission in a Communication System

ABSTRACT

A method is provided for improving synchronization and information transmission in a communication system, including: generating a signal with a centrally symmetric part s(k) exploitable for synchronization; and sending the signal over a communication channel. The signal is based on a uniquely identifiable sequence c(l) from a set of sequences exploitable for information transmission. The centrally symmetric part s(k) is centrally symmetric in the shape of absolute value thereof. The centrally symmetric part s(k) is of arbitrary length N.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/365,957, filed on Feb. 3, 2012, which is a continuation of U.S.patent application Ser. No. 12/175,632, filed on Jul. 18, 2008, which isa continuation of International Patent Application No.PCT/CN2006/000076, filed on Jan. 18, 2006, all of which is herebyincorporated by reference in their entireties.

TECHNICAL FIELD

The present invention relates to a method for synchronization andinformation transmission in a communication system, and moreparticularly to a radio communication system, a transmitter unit and areceiver unit.

BACKGROUND

Several different proposals for the EUTRA synchronization channel (SCH),intended for use in the cell search procedure are proposed in 3^(rd)Generation Partnership Project RAN1 until now. For instance: Motorola,“Cell Search and Initial Acquisition for OFDM Downlink,” R1-051329,Seoul, Korea, Nov. 7-11, 2005 (this paper is called Moto hereinafter).

Compared to the solution existing in the WCDMA standard, Motorola'sproposal makes a step forward towards concurrent initial timingacquisition and cell identification. In this way the duration of overallcell search procedure, resulting in timing acquisition and cellidentification, is supposed to be shortened.

According to this proposal, the synchronization channel consists of twoconcatenated identical cell-specific OFDM waveforms, which are precededby a cyclic prefix of L_(CP) samples. Such SCH is designed to supportthe initial timing acquisition by using blind differential correlationdetection in the receiver, see: T. M. Schmidl and D. C. Cox, “RobustFrequency and Timing Synchronization for OFDM,” IEEE Trans. OnCommunications, Vol. 45, pp. 1613-1621, December 1997 (this paper iscalled T. M. Schmidl hereinafter).

The cell identification is performed after the initial timingacquisition, by detecting the cell specific OFDM waveform obtained bymodulating the sub-carriers with the elements of a cell-specificZadoff-Chu sequence of prime length (the Zadoff-Chu sequences are thebasis for the generation of a much broader family of so-called GCLsequences, see: B. M. Popovic, “Generalized chirp-like polyphasesequences with optimum correlation properties,” IEEE Trans. OnInformation Theory, vol. 38, pp. 1406-1409, July 1992. The cell-specificindex of the GCL sequence can be detected by using an Inverse DiscreteFourier Transform (IDFT), after the differential encoding of the blockof the received signal samples.

Although the above solution for the synchronization channel seems quitepromising in terms of reduced overall cell search time, still its timingacquisition is very sensitive to noise/interference due to the broadtriangular shape of the differential correlation function.

The SCH signal from Moto consists of a cyclic prefix followed by asynchronization signal s(k), k=0, 1, . . . , N−1, consisting of twicerepeated basic cell-specific OFDM waveform W(l), l=0, 1, . . . , N/2−1,where N is the number of samples in the OFDM signal obtained after theIDFT in the transmitter. The timing of the SCH can be detected in thereceiver by the following algorithm:

A) Take a block of N received signal samples;

B) Correlate the first N/2 samples of the block with the complexconjugate of the last N/2 samples of the block, and store the resultingdifferential correlation;

C) Repeat the first two steps for a new block of N samples of thereceived signal, taken after a delay of one sample compared to theprevious block;

D) Find the delay of the block of N samples that result in the maximumcorrelation magnitude, and select it as the initial timing for OFDMsymbol demodulation.

The differential correlation C(p) of the received signal r(k), k=0, 1, .. . , N−1, can be mathematically represented as

$\begin{matrix}{{{C(p)} = {\sum\limits_{k = 0}^{{N/2} - 1}\; {{r\left( {p + k} \right)} \cdot {r^{*}\left( {p + k + {N/2}} \right)}}}},} & (1)\end{matrix}$

where p denotes the delay of the first sample in the block of N receivedsamples with respect to the true position of the first sample of thesynchronization signal, and “*” denotes complex conjugation. If thereceived signal contains just the repeated waveform W(k) (without thecyclic prefix), then it follows that the differential correlation of thereceived signal is equal to the differential correlation functionC_(W)(p) of the waveform W(k), which exists only for p=0, ±1, ±2, . . ., ±(N/2−1), N is even, and is given by

$\begin{matrix}{{{C_{W}(p)} = {{\sum\limits_{k = 0}^{{N/2} - 1 - {p}}\; {{W(k)} \cdot {W^{*}(k)}}} = {\sum\limits_{k = 0}^{{N/2} - 1 - {p}}\; {{W(k)}}^{2}}}},{p = 0},{\pm 1},{\pm 2},{\ldots \pm {\left( {{N/2} - 1} \right).}}} & (2)\end{matrix}$

The differential correlation function of the synchronization signal fromMoto, generated by IFFT of N=128 samples, with cyclic prefix of 10samples, is shown in FIG. 1.

The formula (2) explains the broad triangular-like shape of thedifferential correlation function in FIG. 1. Small distortions of thetriangular shape come from the fluctuations of the signal envelope.Thus, it can be seen from (2) that the differential correlation dependsjust on the envelope of synchronization signal, so the differentsynchronization signals with the constant envelope will produce the samedifferential correlation. The differential correlation function in FIG.1 reaches a plateau which has a length equal to the length of the cyclicprefix (T. M. Schmidl).

The peak detection of the differential correlation can be done, forexample by finding the maximum of the correlation function calculated ina (10 ms) frame of the received samples. However, there might besynchronization signals from multiple cells that can be receivedconcurrently in the user equipment (UE), and all of them should bedetected in the cell search procedure. Consequently, the peak detectionof the differential correlation in a frame of received samples is notenough, because it cannot discriminate the peaks coming from thedifferent cells.

Instead, or additionally, some kind of threshold-based selection has tobe applied. For example, the magnitude of each differential correlationvalue can be compared with an adaptive threshold proportional to theenergy of the signal in the correlation window of N/2 samples used tocalculate the observed correlation value, so all the correlation valueslarger than a certain percentage of the signal energy in thecorresponding correlation window will be selected for further processingby peak detection to find the accurate time of arrival of eachsynchronization signal.

The comparison with the above adaptive threshold is equivalent tocomparing the normalized differential correlation as defined in T. M.Schmidl, eq. (8) (normalized with the received energy in the secondhalf-symbol) with a fixed threshold between 0 and 1. As the timingacquisition performances are basically determined by the properties ofdifferential correlation, we shall not discuss further normalizationwith the signal energy.

An impulse-like differential correlation function is obtained by theOFDM synchronization signal proposed in B. Park et al, “A Novel TimingEstimation Method for OFDM Systems”, IEEE Communications Letters, Vol.7, No. 5, pp. 239-241, May 2003 (this paper is called B. Parkhereinafter), eq. (10) as

s(k)=[W(k)Z(k)W*(k)Z*(k)],  (3)

where the waveform W(k) of length N/4 samples is generated by IFFT of apseudo-noise sequence, while the waveform Z(k) is designed to besymmetric with W(k). The synchronization signal (3) is detected by amodified differential correlation, defined as (B. Park)

$\begin{matrix}{{D(p)} = {\sum\limits_{k = 0}^{{N/2} - 1}\; {{r\left( {p - k} \right)} \cdot {{r\left( {p + k} \right)}.}}}} & (4)\end{matrix}$

The signal (3) is explicitly and exclusively defined as an OFDM signal,to be generated by the IFFT, so the B. Park does not anticipate othertypes of centrally symmetric synchronization signals, such asspread-spectrum direct sequence signals.

If neglect the complex conjugation in the signal (3), a person skilledin the art can notice that it is basically a repetitive signal, whosebasic repeated waveform of length N/2 samples is centrally symmetric.Such a signal has an impulse-like differential correlation function, butits repetitive structure results in high correlation sidelobes, equalalways to the quarter of the signal energy, regardless of the propertiesof the pseudo-noise sequences used to modulate the sub-carriers withinthe OFDM signal. The high correlation sidelobes can cause an increasedprobability of false timing acquisition, so it is desirable to reducethem as much as possible.

Besides, the shorter length (N/2) of the basic waveform repeated in thesynchronization signal (3) implies a smaller number of differentsynchronization signals that can be generated. In the application ofinterest, such as the cell search in a cellular system (which is notconsidered in B. Park), where the synchronization signals should notjust serve for timing acquisition, but also for the informationtransmission, the smaller number of potential different synchronizationsignals with low cross-correlation implies a smaller amount informationthat can be conveyed by the synchronization signal.

Further on, the complex conjugation of the basic repeated waveform inthe second half of the signal might complicate the implementation of thesignal generator and demodulator, especially if the signal is supposedto be obtained by the IDFT of a complex pseudo-noise sequence.

Also, the synchronization signal (3) consists of two symmetricwaveforms, so N/2 is an even number.

In the paper, Zhang et al. “Joint Frame Synchronization and FrequencyOffset Estimation OFDM Systems” IEEE Trans. On Broadcasting, vol. 51, no3, September 2005, is described a joint frame synchronization andcarrier frequency offset estimation scheme. The paper seems mainly beconcentrating on improving the frequency error estimation; it is notsaid how the arrival time of the training symbol should exactly beestimated.

SUMMARY

A method is provided which enables synchronization of a communicationsystem with decreased sensitivity to noise/interference, and which alsoenables a simultaneous transfer of information.

Thus, according to an embodiment of the invention, a signal for improvedsynchronization and information transmission in a communication systemis generated with a centrally symmetric part, s(k), the centrallysymmetric part s(k) being symmetric in the shape of the absolute valuethereof, wherein the centrally symmetric part s(k) is of arbitrarylength N and is based on a uniquely identifiable sequence c(l) from aset of sequences.

The method of the present invention could be implemented through atransmitter unit and in a receiver unit in a communication system.Together they would form part of a radio communication system that wouldinclude at least one such transmitter unit and at least one suchreceiver unit.

The timing acquisition in the receiver is improved in applications wherethe synchronization signals transmitted to support and alleviate thetiming acquisition in the receiver should also carry some information,such as transmitter's identification number, etc. One of suchapplications is cell search procedure in a cellular system. Besides, itallows an increased amount of information to be carried by thesynchronization signals, compared to the prior art in Moto.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, with reference of the appendeddrawings, on which

FIG. 1 illustrates a correlation function according to the prior art;

FIG. 2 illustrates a reverse correlation function;

FIG. 3-FIG. 6 are graphs showing various probabilities for correcttiming acquisition; and

FIG. 7 illustrates a radio communication system according to anembodiment of the present invention.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

In order to achieve an impulse-like differential correlation function,embodiments of the present invention shall first modify the definitionof the differential correlation so that as much as possible differentproducts of samples are involved in the summations corresponding to thedifferent delays. In this way the differential correlation valuescorresponding to different out-of-synchronization delays will berandomized.

One way to achieve the random out-of-sync differential correlationvalues is to reverse the order of samples in one of the blocks ofsamples used in (1). We shall define so-called reverse differentialcorrelation D(p) as

$\begin{matrix}{{{D(p)} = {\sum\limits_{k = 0}^{{\lceil{N/2}\rceil} - 1}\; {{r\left( {p + k} \right)} \cdot {r^{*}\left( {p + N - 1 - k} \right)}}}},} & (5)\end{matrix}$

where p denotes the delay of the first sample in the block of N receivedsamples with respect to the true position of the first sample of thesynchronization signal, and ┌x┐ denotes the ceiling function of x, i.e.the smallest integer greater than or equal to x.

To obtain the maximum possible correlation value (5) at p=0, equal tothe energy of the signal in the correlation window of ┌N/2┐ samples, thesynchronization signal s(k), k=0, 1, . . . , N−1, should be centrallysymmetric, i.e. such that

$\begin{matrix}{{s(k)} = \left\{ {\begin{matrix}{{s\left( {N - 1 - k} \right)},} & {{k = 0},1,\ldots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},} \right.} & (6)\end{matrix}$

where N is arbitrary positive integer, and where we assumed that thesignal energy is equally distributed between the first and second blockof ┌N/2┐ samples.

From (5) and (6) it follows that the reverse differential correlationD_(s)(p) of the synchronization signal s(k) exists only for p=0, ±1, ±2,. . . , ±(┌N/2┐−1), and is given by

$\begin{matrix}\begin{matrix}{{D_{s}(p)} = {D_{s}^{*}\left( {- p} \right)}} \\{= {\sum\limits_{k = 0}^{{\lceil{N/2}\rceil} - 1}\; {{s\left( {p + k} \right)} \cdot {s^{*}\left( {p + N - 1 - k} \right)}}}} \\{= {\sum\limits_{k = p}^{{\lceil{N/2}\rceil} - 1}\; {{s\left( {k + p} \right)} \cdot {s^{*}\left( {k - p} \right)}}}} \\{{= {\sum\limits_{l = 0}^{{\lceil{N/2}\rceil} - 1 - p}\; {{s\left( {l + {2p}} \right)} \cdot {s^{*}(l)}}}},{p = 0},1,\ldots \mspace{14mu},{\left\lceil {N/2} \right\rceil - 1.}}\end{matrix} & (7)\end{matrix}$

The formula (7) resembles very much to the aperiodic autocorrelationfunction R(p) of the synchronization signal s(k), defined as

$\begin{matrix}{{{R(p)} = {{R^{*}\left( {- p} \right)} = {\sum\limits_{l = 0}^{N - 1 - p}\; {{s\left( {l + p} \right)} \cdot {s^{*}(l)}}}}},{p = 0},1,{{\ldots \mspace{14mu} N} - 1.}} & (8)\end{matrix}$

As it can be seen, the only difference between D_(s)(p) and R(p) is in areduced number of summation elements. Thus if the s(k) has animpulse-like aperiodic autocorrelation function, its reversedifferential correlation function has very good chances to beimpulse-like as well.

The equation (7) shows that, in general, the non-repetitive, butcentrally symmetric pseudo-random signals produce lower correlationsidelobes than the repetitive signals.

An alternative to centrally symmetrical synchronization signals definedby (6) are such satisfying

$\begin{matrix}{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - 1 - k} \right)},} & {{k = 0},1,\ldots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},} \right.} & (9)\end{matrix}$

in which case the reverse differential correlation has to be re-definedas

$\begin{matrix}{{D(p)} = {\sum\limits_{k = 0}^{{\lceil{N/2}\rceil} - 1}\; {{r\left( {p + k} \right)} \cdot {{r\left( {p + N - 1 - k} \right)}.}}}} & (10)\end{matrix}$

The OFDM synchronization signal (3) proposed in the prior art, B. Park,eq. (10) can be viewed as a special case of signal (9). Note that (9) ismore general because it is defined for arbitrary length N, while (3) isdefined only for N=0 mod 4.

The same maximum absolute value of the reverse differential correlationcan be obtained if the signal is skew-symmetric, i.e. defined as

$\begin{matrix}{{s(k)} = \left\{ {\begin{matrix}{{- {s\left( {N - 1 - k} \right)}},} & {{k = 0},1,\ldots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix}.} \right.} & (6.1)\end{matrix}$

Similarly, the absolute value of (10) will not change if the signal isdefined as

$\begin{matrix}{{s(k)} = \left\{ {\begin{matrix}{{- {s^{*}\left( {N - 1 - k} \right)}},} & {{k = 0},1,\ldots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix}.} \right.} & (9.1)\end{matrix}$

Embodiment 1

To illustrate the design of centrally symmetric synchronization signals(6) and the properties of the corresponding reverse differentialcorrelation functions (5), we shall generate the set of OFDM centrallysymmetric synchronization signals starting from the assumptions given inMoto: the sampling frequency is 1.92 MHz, the sub-carrier spacing is 15kHz, the maximum number of occupied sub-carriers is Nosc=76 out oftotally N=128 sub-carriers within 1.92 MHz frequency band (thetransmission bandwidth is 1.25 MHz). The occupied sub-carriers aremodulated by the elements of a pseudo-random sequence from the set ofsequences with good cross-correlation properties. The differentsequences from the set are labelled by the different cell identificationnumbers (IDs). After the DFT demodulation of the received OFDM signalthe transmitted sequence can be identified by de-mapping from thesub-carriers, followed by a certain signal processing. Lowcross-correlation between sequences contributes to more reliableidentification of the sequences when multiple signals are concurrentlyreceived from different cells.

The output OFDM synchronization signal s(k) of length N=128 samples isobtained by the IDFT of the spectrum H(n) of N=128 Fourier coefficients,as

$\begin{matrix}{{{s(k)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}\; {{H(n)}W_{N}^{- {kn}}}}}},{W_{N} = {\exp \left( {{- {j2}}\; {\pi/N}} \right)}},{j = \sqrt{- 1}},{k = 0},1,2,\cdots \mspace{14mu},{N - 1.}} & (11)\end{matrix}$

If H(n)=H(N−n), n=0, 1, 2, . . . , N−1, where H(N)=H(0) holds accordingto the periodicity of the DFT, it can be shown that the s(k) will bealso symmetric around its s(N/2) sample, i.e.

s(k)=s(N−k), if and only if H(n)=H(N−n), k,n=1, . . . ,N−1.  (12)

The proof of (12) follows: Starting from the definition of s(k) as

$\begin{matrix}{{{s(k)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}\; {{H(n)}W_{N}^{- {kn}}}}}},{W_{N} = {\exp \left( {{- {j2}}\; {\pi/N}} \right)}},{j = \sqrt{- 1}},{k = 0},1,2,\cdots \mspace{14mu},{N - 1.}} & ({A1})\end{matrix}$

it follows

$\begin{matrix}{\begin{matrix}{{s\left( {N - k} \right)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}\; {{H(n)}W_{N}^{kn}}}}} \\{= {\frac{1}{N}{\sum\limits_{t = N}^{1}\; {{H\left( {N - l} \right)}W_{N}^{- {kl}}}}}} \\{= {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{H\left( {N - l} \right)}W_{N}^{- {kl}}}}}}\end{matrix}{{k = 0},1,2,\cdots \mspace{14mu},{N - 1},}} & ({A2})\end{matrix}$

where we introduced the change of variables n=N−l, reordered thesummation and used periodicity of the DFT (H(n)=H(n+N)). From (A.1) and(A.2) it follows that s(k)=s(N−k) if H(n)=H(N−n), what is a sufficientcondition. It is also a necessary condition, meaning that only ifH(n)=H(N−n) it will be s(k)=s(N−k), as it can be shown by starting fromthe expression for H(n).

The spectrum H(n) might be obtained by using the elements of apseudo-random sequence c(l), l=0, 1, . . . , L−1, L≦Nosc, as the Fouriercoefficients at the occupied sub-carrier frequencies.

If we define the mapping between c(l) and H(n) as

$\begin{matrix}{{H(n)} = \left\{ \begin{matrix}{{c\left( {n + \frac{L - 1}{2}} \right)},} & {{n = 0},1,2,\cdots \mspace{14mu},\frac{L - 1}{2}} & \; \\{{c\left( {n - N + \frac{L - 1}{2}} \right)},} & {{n = {N - \frac{L - 1}{2}}},\cdots \mspace{14mu},{N - 1},} & {{L\mspace{14mu} {is}\mspace{14mu} {odd}},} \\{0,} & {{n = {\frac{L - 1}{2} + 1}},\cdots \mspace{14mu},{N - \frac{L - 1}{2} - 1}} & \;\end{matrix} \right.} & (13)\end{matrix}$

where c(l), l=0, 1, . . . , L−1, is a centrally symmetric sequence ofodd length L, it is obvious that condition in (12) will be satisfied.

Consequently, the resulting synchronization signal s(k), k=0, 1, 2, . .. , N−1, is a low-pass base-band OFDM signal symmetrical around itss(N/2) sample, meaning that only the sample s(0) does not have itssymmetrical counterpart with respect to s(N/2). In other words, theresulting OFDM synchronization signal can be considered as consisting oftwo parts: the first part contains one sample and the second partcontains N−1 centrally symmetric samples, such that s(k)=s(N−k), k=1, 2,. . . , N−1.

It further means that for the blind detection of the above OFDM signalwe should use the blocks of N−1 input signal samples, and perform thereversed differential correlation as

$\begin{matrix}{{D(p)} = {\sum\limits_{k = 0}^{{\lceil{N/2}\rceil} - 1}\; {{r\left( {p + k + 1} \right)} \cdot {{r^{*}\left( {p + N - 1 - k} \right)}.}}}} & (14)\end{matrix}$

However, the whole block of N samples should be used for OFDMdemodulation, and subsequent identification of the information content(cell ID), once the correct timing is acquired.

The remaining question is which kind of centrally symmetric sequences ofodd length L to choose for modulation of the sub-carriers. The L−1pseudo-noise sequences {a_(r)(l)}, r=1, . . . , L−1, where L is a primenumber, used in Moto to produce the repetitive OFDM synchronizationsignals are Zadoff-Chu (ZC) sequences of odd length L, defined as

a _(r)(l)=W _(L) ^(rl(l+1)/2) , l=0,1, . . . ,L−1, L is odd,  (15)

where W_(L)=exp(−j2π/L), j=√{square root over (−1)}.

If L is odd, it can be easily shown that the ZC sequence (15) iscentrally symmetric (around its (L−1)/2+1-th element), i.e.a_(r)(l)=a_(r)(L−1−l), l=0, 1, . . . , L−1. To accommodate the sequencelength to be equal or less than the maximum number of occupiedsub-carriers, we can discard a certain number sequence elements at thebeginning and at the end of the ZC sequence so that the resultingshortened sequence remains centrally symmetrical.

As the maximum allowed number of occupied sub-carriers is Nosc=76, andthe ZC sequence length should be a prime number, we shall use L=79 in(15) to generate a prototype ZC sequence, which is then shortened tolength L=75 by discarding the first 2 and the last 2 elements of theprototype ZC sequence, so that the resulting shortened ZC sequenceremains centrally symmetric. The shortened sequence is then used in (13)to produce the OFDM synchronization signal (11) after IDFT of H(n).

By choosing the different values of r in (15), we can obtain up toM=L−1=74 different OFDM synchronization signals, each carrying thedifferent information about the cell ID. This number of cell IDs isalmost twice larger than the number (41) of cell IDs in Moto for thesame size of synchronization signals. In the same time, the principle ofthe detection of the ZC sequences from Moto, by using differentialencoding and IDFT, can be applied also in the example at hand.

To ensure the demodulation robustness in the case of multipathpropagation channel, the OFDM synchronization signal is preceded by acyclic prefix. The magnitude of the reverse differential correlationfunction of the OFDM synchronization signal (11) obtained from theshortened ZC sequence of length L=75, with the cell ID=r=29 and with thecyclic prefix of L_(CP)=10 samples, is shown in FIG. 2.

The cyclic prefix makes the reverse differential correlation functionasymmetrical, with slightly increased sidelobe levels for the negativedelays. However, as the sidelobe levels are still relatively lowcompared to the main peak, the probability of the false timingacquisition is not expected to be influenced by them.

The Zadoff-Chu sequences are the basis for the generation of the GCLsequences {c(l)}, defined as [6]

c(l)=a(l)b(l mod m), l=0,1, . . . ,L−1,  (16)

where L=sm², s and m are positive integers, {b(l)} is a sequence with mcomplex numbers of unit magnitude, and {a(l)} is a Zadoff-Chu sequenceof length L. So, in order to obtain a centrally symmetric GCL sequence,L should be odd and the modulation sequence {b(l)} should be centrallysymmetric. The centrally symmetric GCL sequences have a potential formore information transmission if used in the present invention, becauseof their larger number. Besides, they retain the optimum correlationproperties independently of the selection of their modulation sequences.

Timing Acquisition Performances

In the user equipment (UE) in cellular systems the initial frequencyerror (immediately after power on) of the RF signal might be of theorder of tens of thousands of Hz. This frequency error will be reducedwithin the limits of several hundreds of Hz once the receiver is lockedto the received signal from a base station. The UE will be locked to abase station after the initial cell search, the task performed by the UEafter it is switched on. Once the UE has found its “camping” cell, thecell search procedure enters the monitoring mode, where it monitors theavailable neighbouring cells, either for possible handover, if the UE isin active mode, or for possible cell re-selection (for better signalreception), if the UE is in the idle mode. In the monitoring mode thefrequency error between the received signals and the UE's RF signal issignificantly reduced because all the cells are tightly frequencysynchronised and the UE is already synchronized to one of them.

Thus, during the initial cell search it should be possible to detect thetime-of-arrival of the synchronization signals transmitted from the basestation under relatively high frequency error in the receiver.

The timing acquisition performance of the synchronization signal fromthe Embodiment 1 is evaluated by simulation, in terms of probability ofcorrect timing acquisition as a function of signal-to-noise ratio (SNR)on Additive White Gaussian Noise (AWGN) channel. The four values of theinitial frequency error df between the UE and the base station aresimulated: df=0, 1, 2 and 3 ppm at 2.6 GHz carrier frequency. The cyclicprefix is 10 samples long in all cases.

The timing acquisition is considered correct if the estimated time ofarrival is within the error tolerance zone, which is positioned beforethe true timing position, so that it overlaps the cyclic prefix in theOFDM signal. The size of the error tolerance zone cannot be larger thanthe length of the cyclic prefix, and should be equal to the part of thecyclic prefix that is not covered by the channel response of theprevious OFDM symbol. As the length of cyclic prefix should not be muchlonger (if at all) than the maximum expected length of the channelresponse, the error tolerance zone in practice cannot be longer than afew samples. However, as the repetitive synchronization signal from Motois evaluated as the reference for comparison, we shall take the errortolerance zone to be equal to the cyclic prefix, in order to obtain thebest performances for the signal from Moto.

It can be easily known that the magnitude of the differentialcorrelation does not depend on the frequency error, so the signal fromMoto is evaluated with no frequency error. The results are shown in FIG.3.

Without the initial frequency error, the centrally symmetric signaldetected by the reverse differential correlation outperforms therepetitive signal detected by the differential correlation by more than1 dB at 0.5 probability of correct acquisition, and more than 5 dB at0.9 probability of correct acquisition.

For the non-zero values of the frequency error, the performance of therepetitive signal remains unchanged, while the performance of thecentrally symmetric signal deteriorates with increase of the frequencyerror. At the frequency error of 1 ppm (2600 Hz), the relativeperformances remain almost unchanged. At the frequency error of 2 ppm,the centrally symmetric signal still remains better at probabilities ofcorrect acquisition above 0.5, although the repetitive signal becamebetter at very low SNRs. However, at the frequency error of 3 ppm thecentrally symmetric signal fails to acquire the timing synchronizationregardless of the SNR. This is because some of the sidelobes of thereverse differential correlation become higher than the main lobe, evenwithout the presence of noise.

Embodiment 2

The timing acquisition performance results for the signals fromEmbodiment 1 has demonstrated that if the frequency error is above acertain threshold, the differential correlation produces better timingacquisition than the reverse differential correlation, while below acertain frequency error it is opposite.

This result suggests that if the frequency error during the initial cellsearch is above 2 ppm, it would be beneficial that the synchronizationsignal is both centrally symmetric and periodic. Such a signal could bedetected in the UE both by the differential correlation and the reversedifferential correlation, depending on UE's cell search mode, i.e.depending on the maximum expected frequency error in between the carrierfrequency of received signal and the frequency of the reference RFsignal in the receiver.

Thus, the initial cell search the synchronization signals transmittedfrom the base stations should be performed by using the differentialcorrelation. Once the cell search enter the monitoring mode, thesynchronization signals can be detected by the reverse differentialcorrelation, which provide much better timing acquisition performancesif the frequency error is low, allowing a faster detection of theneighbouring cells. It should be noted that in the cell searchmonitoring mode a quick detection of the neighbouring cells with bettersignal quality reduces the interference in the system because it allowsUE to transmit will lower power.

Assuming the same conditions as in Embodiment 1, the set of centrallysymmetric and periodic OFDM synchronization signals can be generatedfrom the set of 36 ZC sequences of prime length L=37, by using themapping (13), and IDFT (11), where N=64. The signal of length 64 samplesobtained by (11) is then periodically extended, i.e. repeated to producethe final centrally symmetric and periodic synchronization signal oflength 128 samples. As in the previous example, in the resulting signals(k) of length N=128 samples, only the sample s(0) does not have itssymmetrical counterpart with respect to s(N/2).

The same signal can be obtained directly (without periodic extension) byusing (11) and the following general mapping

$\begin{matrix}{{H(n)} = \left\{ \begin{matrix}{{c\left( {\frac{n}{R} + \frac{L - 1}{2}} \right)},} & {{n = 0},R,{2R},\cdots \mspace{14mu},{\left( \frac{L - 1}{2} \right)R}} & \; \\{{c\left( {\frac{n - N}{R} + \frac{L - 1}{2}} \right)},} & \begin{matrix}{{n = {N - {\left( \frac{L - 1}{2} \right)R}}},} \\{{N - {\left( \frac{L - 3}{2} \right)R}},\cdots \mspace{14mu},{N - R},}\end{matrix} & {{L\mspace{14mu} {is}\mspace{14mu} {odd}},} \\{0,} & {elsewhere} & \;\end{matrix} \right.} & (17)\end{matrix}$

where c(l), l=0, 1, . . . , L−1, is a centrally symmetric sequence ofodd length L, R=2 is the number of repetitions, i.e. periods of acertain basic waveform within the signal, and N=128 is the IFFT size. Ingeneral, the mapping (17) produce a centrally symmetric signal with Rperiods if N mod R=0.

The timing acquisition performance of the above synchronization signalis evaluated by simulation, in terms of probability of correct timingacquisition as a function of signal-to-noise ratio (SNR) on AdditiveWhite Gaussian Noise (AWGN) channel. The four values of the initialfrequency error df between the UE and the base station are simulated:df=0, 1, 2 and 3 ppm at 2.6 GHz carrier frequency. The cyclic prefix is10 samples long in all cases. The results are shown in FIG. 4.

From FIG. 3 and FIG. 4 it can be seen that the reverse differentialcorrelation of centrally symmetric and periodic OFDM signal is morerobust to the frequency error of 3 ppm than the reverse differentialcorrelation function of the non-periodic OFDM signal. Starting from thesimilarity between the formulas (7) and (8), the explanation of thedifferent timing acquisition performances in FIG. 3 and FIG. 4 can bederived from the properties of the generalized aperiodic autocorrelationfunctions of the corresponding signals, widely known as the ambiguityfunction. This function is a two-dimensional function of the delay andthe frequency error.

It is well known that the chirp-like signals, such as the non-repetitivesignal from FIG. 3, has the ridge-type ambiguity function, distinguishedby a shifted, non-zero delay position of its main lob at a highfrequency error. This effect is the major reasons for the collapse ofthe reverse differential correlation at 3 ppm frequency error. Thesignals with some other cell IDs might be a bit less sensitive to thiseffect and might converge to probability of acquisition equal to 1 athigher SNRs, but they will also collapse at a bit higher frequencyerrors.

On the other side, the periodic signals, such as the one from FIG. 4,have so-called bed-of-nails type ambiguity functions, distinguished byrather high sidelobes regularly placed in the time-frequency plane, butthe position of the main lobe, corresponding to the zero delay isunchanged with the frequency. Basically, these signals behave asvirtually having the shorter length, what results in less distortion athigh frequency error. On the other side, the high sidelobes of thereverse differential correlation come from the repetitive nature of thesignal, so that even when there is no frequency error, the signalconsisting of two periods of the same basic waveform has the reversedifferential correlation sidelobes equal at least to the half of themain lobe. This results in a loss of acquisition performances for lowfrequency errors (bellow 2 ppm), as it can be noticed by comparing theFIG. 3 and FIG. 4.

Embodiment 3

As abovementioned, the error tolerance zone in practice cannot be longerthan a few samples. In that case, however, even the differentialcorrelation (used to detect the repetitive synchronization signal fromMoto) shows rather bad performances at high frequency errors, as it canbe seen in FIG. 5, where the timing acquisition performances of thesignals from FIG. 3 are evaluated with the tolerance zone of 2 samples.

The reason for bad performances of the differential correlation lies inthe plateau shown in FIG. 1, which makes it highly probable that thenoise will produce a correlation peak at the delay within thecorrelation plateau less than the zero (correct) delay. Thus, the curvecorresponding to repetitive signal converges very slowly to the value 1with an increase of SNR.

The previous discussion about the different types of the ambiguityfunctions leads to consideration of other types of the pseudo-noisesequences, with ambiguity functions more tolerant to frequency errors.Such pseudo-noise sequences are, for example, the sets of orthogonalGolay (binary) complementary sequences, see M. J. E. Golay,“Complementary Series”, IRE Transactions on Information Theory, Vol.IT-7, pp. 82-87, April 1961 (this paper is called Document 8hereinafter). The pairs of complementary Golay sequences exist for evensequence lengths L, and are distinguished by the property that the sumof the aperiodic autocorrelation functions of the sequences equals zerofor all non-zero delays. A set of orthogonal Golay sequences of length Lcan be obtained by the bit-wise multiplication of a single Golaycomplementary sequence of length L with all L Walsh sequences of lengthL [Document 8]. The sequences within such a set can be grouped into L/2different complementary pairs.

If the bits of a Golay sequence from the set of orthogonal Golaycomplementary pairs are used as the Fourier coefficients H(n) in (11),the resulting OFDM synchronization signal s(k) is similar to (9) and hasthe property:

$\begin{matrix}{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - k} \right)},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix}.} \right.} & (18)\end{matrix}$

Such a signal can be detected by a modified reversed differentialcorrelation (10), as

$\begin{matrix}{{D(p)} = {\sum\limits_{k = 0}^{{\lceil{N/2}\rceil} - 1}{{r\left( {p + k + 1} \right)} \cdot {{r\left( {p + N - 1 - k} \right)}.}}}} & (19)\end{matrix}$

It can be easily known that the magnitudes of the reversed differentialcorrelations (10) and (19) remain unchanged under arbitrary frequencyerror in the signal received over a single-path propagation channel.This is a general property that is valid for arbitrary signals (9),(9.1) and (18).

If the elements of a Golay sequence c(k) are mapped as the Fouriercoefficients of the equidistant consecutive sub-carriers, for example as

$\begin{matrix}{{H(n)} = \left\{ \begin{matrix}{{c\left( {n + {L/2}} \right)},} & {{n = 0},1,2,\cdots \mspace{14mu},{{L/2} - 1}} \\{{c\left( {n - N + {L/2}} \right)},} & {{n = {N - {L/2}}},\cdots \mspace{14mu},{N - 1},{L\mspace{14mu} {is}\mspace{14mu} {even}},} \\{0,} & {elsewhere}\end{matrix} \right.} & (20)\end{matrix}$

the resulting OFDM signal has the peak-to-average power ratio less than3 dB, see B. M. Popovic, “Synthesis of Power Efficient Multitone Signalswith Flat Amplitude Spectrum”, IEEE Transactions on Communications, Vol.39, No. 7, pp. 1031-1033, July 1991. It further means that all the OFDMsynchronization signals, based on different Golay sequences from a setof orthogonal complementary pairs will have a small PAPR values,allowing in that way the maximization of the average transmitted power,i.e. the maximization of the received SNR at the cell edge.

The timing acquisition performances of an OFDM signal obtained from aGolay complementary sequence of length L=64 mapped according to (20) and(11) into an OFDM signal of length N=128, are shown in FIG. 6. It can beseen that the timing acquisition performances of the OFDM signalobtained from a Golay complementary sequence do not change with theincrease of the frequency error.

Information embedding in this scenario can for instance be accomplishedby labelling each of the orthogonal Golay sequences in the present set.After receiving the signal and demodulating the data from the OFDMsignal, the specific sequence could be identified by correlating withall sequences in the present set. Such a bank of correlators can beefficiently implemented, for example, by using the fast Hadamardtransformation. Differential encoding might be applied to thedemodulated sequence before correlation to remove the channeldistortion. In that case the reference sequences used for correlationshould be also differentially encoded.

Now with reference to FIG. 7, an embodiment of the present inventionalso provides a radio communication system, which for instance couldconsist of base station(s) 120 of a cellular system 100 and terminal(s)130 communicating with the base station(s). The base station(s) and/orterminal(s) would include at least one transmitter unit with means forgenerating and sending a signal with a centrally symmetric part, s(k),wherein the centrally symmetric part s(k) is of arbitrary length N. Thebase station(s) and/or terminal(s) would also include at least onereceiver unit including means for receiving and processing signalsgenerated by the transmitter unit.

Applications and Alternatives

The present invention can be used in all applications wheresynchronization signals are transmitted to support and alleviate timingacquisition in a receiver and also when the signals are carrying someinformation, such as a transmitter's identification number, etc. One ofsuch applications is cell search procedure in the cellular systems.

The proposed centrally symmetric synchronization signals can be of OFDMtype, which brings certain benefits for the demodulation of theinformation from the signal which has passed multi-path(time-dispersive) propagation channel.

However, the noise-like centrally symmetric synchronization signals ofother types, such as direct-sequence spread-spectrum signals, detectedby the reverse differential correlation, can also be deployed with thesimilar timing acquisition performances.

What is claimed is:
 1. A communication system for improvingsynchronization and information transmission, comprising: a transmitter,configured to generate a signal with a centrally symmetric part s(k)exploitable for synchronization, and send the signal over acommunication channel; a receiver, configured to receive the signal;wherein the signal is based on a uniquely identifiable sequence c(l)from a set of sequences exploitable for information transmission, thecentrally symmetric part s(k) is centrally symmetric in the shape ofabsolute value thereof, and the centrally symmetric part s(k) is ofarbitrary length N.
 2. The communication system according to claim 1,wherein the signal is based on a sequence c(l) exploitable forinformation transmission from the transmitter to the receiver, thesequence c(l) is a Zadoff-Chu sequence defined as c(l)=W_(L)^(rl(l+1)/2), l=0, 1, . . . , L−1, L is odd, where W_(L)=exp(−j2π/L),j=√{square root over (−1)} and the sequence c(l) is mapped to a cellidentification number.
 3. The communication system according to claim 1,wherein elements of the sequence c(l) are used for modulatingsub-carriers occupied by the signal.
 4. The communication systemaccording to claim 1, wherein the centrally symmetric part s(k) is oneof the following: ${s(k)} = \left\{ {\begin{matrix}{{s\left( {N - 1 - k} \right)},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - 1 - k} \right)},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s\left( {N - 1 - k} \right)}},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s^{*}\left( {N - 1 - k} \right)}},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s\left( {N - k} \right)},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - k} \right)},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s\left( {N - k} \right)}},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{{and}{s(k)}} = \left\{ {\begin{matrix}{{- {s^{*}\left( {N - k} \right)}},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix}.} \right.}} \right.}} \right.}} \right.}} \right.}} \right.}} \right.}} \right.$5. The communication system according to claim 1, wherein the centrallysymmetric part s(k) is preceded by a cyclic prefix of L_(CP) samplesbeing identical to the last L_(CP) samples of the centrally symmetricpart s(k).
 6. The communication system according to claim 1, wherein thecentrally symmetric part s(k) is obtained as inverse discrete fouriertransform (IDFT) of a spectrum H(n) of N sub-carrier weights, thespectrum H(n) being generated by using elements of the sequence c(l),]l=0, 1, . . . , L−1, L≦N, as Fourier coefficients at sub-carrierfrequencies occupied by the signal.
 7. The communication systemaccording to claim 6, wherein H(n)=H(N−n), n=0, 1, 2, . . . , N−1, whereH(N)=H(0) holds according to the periodicity of discrete fouriertransform (DFT).
 8. The communication system according to claim 6,wherein the sequence c(l) is mapped on to the spectrum H(n) as${H(n)} = \left\{ {\begin{matrix}{{c\left( {n + \frac{L - 1}{2}} \right)},} & {{n = 0},1,2,\cdots \mspace{14mu},\frac{L - 1}{2}} & \; \\{{c\left( {n - N + \frac{L - 1}{2}} \right)},} & {{n = {N - \frac{L - 1}{2}}},\cdots \mspace{14mu},{N - 1},} & \; \\{0,} & {{n = {\frac{L - 1}{2} + 1}},\cdots \mspace{14mu},{N - \frac{L - 1}{2} - 1}} & \;\end{matrix}.} \right.$
 9. The communication system according to claim6, wherein the sequence c(l) is mapped on to the spectrum H(n) as${H(n)} = \left\{ {\begin{matrix}{{c\left( {\frac{n}{R} + \frac{L - 1}{2}} \right)},} & {{n = 0},R,{2R},\cdots \mspace{14mu},{\left( \frac{L - 1}{2} \right)R}} & \; \\{{c\left( {\frac{n - N}{R} + \frac{L - 1}{2}} \right)},} & \begin{matrix}{{n = {N - {\left( \frac{L - 1}{2} \right)R}}},} \\{{N - {\left( \frac{L - 3}{2} \right)R}},\cdots \mspace{14mu},{N - R},}\end{matrix} & \; \\{0,} & {elsewhere} & \;\end{matrix},} \right.$ where R is the number of periods of a certainbasic waveform within the signal, such that N mod R=0.
 10. Thecommunication system according to claim 1, the receiver is furtherconfigured to: calculate and store a reverse differential correlationD(p) from a block of N samples of the signal, repeat, a number of times,the calculate and store step for a new block of N samples of the signal,taken after a delay of one sample compared to the previous block, findthe delay of the block of N samples that result in a maximum correlationmagnitude, select such a delay as the initial timing for demodulation,and detect the unique sequence c(l) from the set of sequences.
 11. Amethod of synchronization in a communication system, comprising:generating a signal with a centrally symmetric part s(k) exploitable forsynchronization; sending the signal over a communication channel; andreceiving the signal; wherein the signal is based on a uniquelyidentifiable sequence c(l) from a set of sequences exploitable forinformation transmission, the centrally symmetric part s(k) is centrallysymmetric in the shape of absolute value thereof, and the centrallysymmetric part s(k) is of arbitrary length N.
 12. The method accordingto claim 11, wherein the signal is based on a sequence c(l) exploitablefor information transmission from the transmitter to the receiver, thesequence c(l) is a Zadoff-Chu sequence defined as c(l)=W_(L)^(rl(l+1)/2), l=0, 1, . . . , L−1, L is odd, where W_(L)=exp(−j2π/L),j=√{square root over (−1)}, and the sequence c(l) is mapped to a cellidentification number.
 13. The method according to claim 11, whereinelements of the sequence c(l) are used for modulating sub-carriersoccupied by the signal.
 14. The method according to claim 11, whereinthe centrally symmetric part s(k) is one of the following:${s(k)} = \left\{ {\begin{matrix}{{s\left( {N - 1 - k} \right)},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - 1 - k} \right)},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s\left( {N - 1 - k} \right)}},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s^{*}\left( {N - 1 - k} \right)}},} & {{k = 0},1,\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s\left( {N - k} \right)},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{s^{*}\left( {N - k} \right)},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{s(k)} = \left\{ {\begin{matrix}{{- {s\left( {N - k} \right)}},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix},{{{and}{s(k)}} = \left\{ {\begin{matrix}{{- {s^{*}\left( {N - k} \right)}},} & {{k = 1},\cdots \mspace{14mu},{N - 1}} \\{0,} & {elsewhere}\end{matrix}.} \right.}} \right.}} \right.}} \right.}} \right.}} \right.}} \right.}} \right.$15. The method according to claim 11, wherein the centrally symmetricpart s(k) is preceded by a cyclic prefix of L_(CP) samples beingidentical to the last L_(CP) samples of the centrally symmetric parts(k).
 16. The method according to claim 11, wherein the centrallysymmetric part s(k) is obtained as inverse discrete fourier transform(IDFT) of a spectrum H(n) of N sub-carrier weights, the spectrum H(n)being generated by using elements of the sequence c(l),] l=0, 1, . . . ,L−1, L≦N, as Fourier coefficients at sub-carrier frequencies occupied bythe signal.
 17. The method according to claim 16, wherein H(n)=H(N−n),n=0, 1, 2, . . . , N−1, where H(N)=H(0) holds according to theperiodicity of discrete fourier transform (DFT).
 18. The methodaccording to claim 16, wherein the sequence c(l) is mapped on to thespectrum H(n) as $(n) = \left\{ {\begin{matrix}{{c\left( {n + \frac{L - 1}{2}} \right)},} & {{n = 0},1,2,\cdots \mspace{14mu},\frac{L - 1}{2}} & \; \\{{c\left( {n - N + \frac{L - 1}{2}} \right)},} & {{n = {N - \frac{L - 1}{2}}},\cdots \mspace{14mu},{N - 1},} & \; \\{0,} & {{n = {\frac{L - 1}{2} + 1}},\cdots \mspace{14mu},{N - \frac{L - 1}{2} - 1}} & \;\end{matrix}.} \right.$
 19. The method according to claim 16, whereinthe sequence c(l) is mapped on to the spectrum H(n) as${H(n)} = \left\{ {\begin{matrix}{{c\left( {\frac{n}{R} + \frac{L - 1}{2}} \right)},} & {{n = 0},R,{2R},\cdots \mspace{14mu},{\left( \frac{L - 1}{2} \right)R}} & \; \\{{c\left( {\frac{n - N}{R} + \frac{L - 1}{2}} \right)},} & \begin{matrix}{{n = {N - {\left( \frac{L - 1}{2} \right)R}}},} \\{{N - {\left( \frac{L - 3}{2} \right)R}},\cdots \mspace{14mu},{N - R},}\end{matrix} & \; \\{0,} & {elsewhere} & \;\end{matrix},} \right.$ where R is the number of periods of a certainbasic waveform within the signal, such that N mod R=0.
 20. The methodaccording to claim 11, further comprising: calculate and store a reversedifferential correlation D(p) from a block of N samples of the signal;repeat, a number of times, the calculate and store step for a new blockof N samples of the signal, taken after a delay of one sample comparedto the previous block; find the delay of the block of N samples thatresult in a maximum correlation magnitude; select such a delay as theinitial timing for demodulation; and detect the unique sequence c(l)from the set of sequences.